3 Answers
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Draft is principally an American English variant that, like many other such simplified spellings, has entered the British English lexicon as an increasingly acceptable alternative spelling. Draft is also considered the standard British English spelling for certain definitions such as a technical drawing, a preliminary or rough version, or the act or result of "drawing" from or upon something (e.g. a Military Draft.)

Draughty is preferable for British English as this is the more common spelling when referring to a current of air.